Motivated by a classical result concerning the ε-subdifferential of the sum of two proper, convex and lower semicontinuous functions, we give in this paper a similar result for the enlargement of the sum of two maximal monotone operators defined on a Banach space. This is done by establishing a necessary and sufficient condition for a bivariate inf-convolution formula.

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...

The use of large amounts of distributed and heterogeneous information has become extremely cumbersome; this difficulty is mainly related to exploring the data, rather than actually storing or exchanging it. The user who is interested in small bits of information is getting more and more confused when having to dig under a large volume of diverse and more importantly semi-structured data. In thi...

where H is the mean curvature of the immersion and K its Gauss curvature. This functional models the elastic energy of thin shells. Willmore studied in [7] the functional W0, by now called Willmore functional. First we note that Wγ(Γ) ≥ 0 holds for every γ ∈ [0, 1]. Let κ1, κ2 ∈ R denote the principal curvatures of the surface. Then H − γK = 1 4 (κ1 + κ2) 2 − γκ1 · κ2 = 1−γ 4 (κ1 + κ2) 2 + γ 4 ...

Automatic attribute discovery methods have gained in popularity to extract sets of visual attributes from images or videos for various tasks. Despite their good performance in some classification tasks, it is difficult to evaluate whether the attributes discovered by these methods are meaningful and which methods are the most appropriate to discover attributes for visual descriptions. In its si...

Background. We explore the nature and aspects of the information needs of informal carers. A comprehensive understanding of these needs is important because it is the first step to meeting these needs effectively. Aim. We report on an empirical validation of a framework for understanding the information needs of carers, composed of four need states: recogniseddemanded, recognised-undemanded, un...

In this paper, we propose the use of spans in addition to edges in noun compound analysis. A span is a sequence of words that can represent a noun compound. Compared with edges, spans have good properties in terms of semi-supervised parsing. They can be reliably extracted from a huge amount of unannotated text. In addition, while the combinations of edges such as sibling and grandparent interac...

This paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous, contra-irresolute and contra semi-continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in L-fuzzy topological spaces. Later, composition and union between these multifunctions have been studied. AMS (MOS) Subject Cla...

A nonconvex generalized semi-infinite programming problem is considered involving parametric max-functions in both, the objective and the constraints. For a fixed vector of parameters, the values of these parametric max-functions are given as optimal values of convex quadratic programming problems. Assuming that for each parameter the parametric quadratic problems satisfy the strong duality rel...